In this paper we characterize the weakly connected independent and weakly connected total dominating sets in the lexicographic product graphs. The weakly connected independent and weakly connected… Expand

Let G = (V (G), E(G)) be a connected undirected graph. The closed neighborhood of any vertex v ∈ V (G) is NG[v] = {u ∈ V (G) : uv ∈ E(G)} ∪ {v}. For C ⊆ V (G), the closed neighborhood of C is N [C] =… Expand

Let G = (V (G),E(G)) be a connected undirected graph. The closed neighborhood of any vertex v ∈ V (G) is NG[v] = {u ∈ V (G) : uv ∈ E(G)} ∪ {v}. For C ⊆ V (G), the closed neighborhood of C is N [C] =… Expand

In this paper we characterize the weakly connected dominating sets in the lexicographic product of two connected graphs. From these characterization, we easily determine the weakly connected… Expand